Time-frequency Analysis of two-wavelet theory in Weinstein setting

Abstract

In this paper, we introduce the notion of Weinstein two-wavelet and we define the two-wavelet localization operators in the setting of the Weinstein theory. Then we give a host of sufficient conditions for the boundedness and compactness of the two-wavelet localization operator on L p α (R d+1 + ) for all 1 ≤ p ≤ ∞, in terms of properties of the symbol σ and the functions ϕ and ψ. In the end, we study some typical examples of the Weinstein two-wavelet localization operators.